I know a person who exists.
Is it incumbent upon me or that person to prove they exist to you?
You. You're the one making the claim.
If I speak of their existence, would this also be anecdotal and hearsay and unnaccepted?
If all you do is speak / make claims, then yes it's anecdotal / hearsay.
How acceptable your anecdote is, depends how you describe said person.
For starters, humans demonstrably exist.
So the mere claim that "some specific human" exists is not at all an extra-ordinary claim.
However, if you then go on to describe this human as having super-powers, like being able to shoot laser beams with his eyes, then clearly you find yourself in very different territory.
That's not a claim that is acceptable at mere face value. The more extra-ordinary the claim, the stronger your evidence needs to be. Seems rather obvious.
I'll give you an example I like to use a lot.
Suppose I tell you that I saw a movie last night starring Jessica Alba.
Likely, you'll have no issue with that. You won't ask me for example to give you photographic evidence of me sitting in my couch, watching that movie.
Because you know movies exist, that Jessica Alba is an actress that stars in many movies and that people watch movies regularly. It's not an extra ordinary claim at all.
Now, suppose I go on to describe how at some point Jessica Alba crawled out of the TV set, made love to me and then crawled back into the TV to finish the movie...
Would you still find that an acceptable claim? Or would you now require solid evidence before you would deem such a claim as being acceptable?
I'll go ahead and assume that yes, you would need such evidence. In fact, more then likely you'll just assume that I am either lying or just crazy and hallucinating.
Now consider your God claim. That's a mega extra-ordinary claim. There are no verifiable instance of anything supernatural. There are no precedents of any such beings whatsoever. There are only claims and anecdotes.
So, all this just to make clear to you that not all claims are on equal footing.
For some claims, mere anecdote / testimony will be enough.
For others, solid evidence is absolutely required.
How much evidence, and how solid it should be, is directly proportional to how outlandish the claim is.